Coherence Map — Electromagnetism
TriadicFrameworks /docs/theories/electromagnetism/coherence_map.md#
EM = coherent behavior of the electromagnetic field.
Maxwell operators = structural constraints, not force laws.
Light = self‑consistent field propagation.
This file defines how electromagnetic coherence is evaluated across operators, fields, geometry, and RTT regimes.
1. Coherence Dimensions#
Electromagnetic coherence has five structural dimensions:
1.1 Divergence Coherence#
Stability of divergence operators.
Coherent when:
- ∇·E = ρ/ε₀ holds structurally
- ∇·B = 0 remains valid
- charge/current sources remain compatible
1.2 Curl Coherence#
Stability of curl operators.
Coherent when:
- ∇×E = −∂B/∂t remains consistent
- ∇×B = μ₀J + μ₀ε₀∂E/∂t remains valid
- time‑variation remains geometrically consistent
1.3 Propagation Coherence#
Stability of wave evolution.
Coherent when:
- propagation is self‑consistent
- no medium (ether) is required
- wavefronts remain stable
- propagation respects geometry
1.4 Source Coherence#
Stability of charge/current as field‑source operators.
Coherent when:
- ρ and J remain structurally valid
- sources do not violate divergence/curl constraints
- no particle‑centric drift is introduced
1.5 Geometric Coherence#
Compatibility of EM fields with spacetime geometry.
Coherent when:
- field tensor Fᵤᵥ is valid
- invariants (FᵤᵥFᵘᵛ, Fᵤᵥ⋆Fᵘᵛ) remain stable
- propagation follows curvature
- EM integrates with GR and QFT
2. Coherence Levels (C0 → C4)#
Coherence is evaluated on a five‑level structural scale:
C0 — Incoherent#
- divergence invalid
- curl invalid
- propagation unstable
- geometry incompatible
System cannot support EM behavior.
C1 — Weak Coherence#
- divergence marginal
- curl noisy
- propagation fragile
EM behavior possible but unstable.
C2 — Moderate Coherence#
- divergence stable
- curl valid
- propagation consistent
EM behavior functional.
C3 — Strong Coherence#
- divergence/curl fully consistent
- propagation stable
- sources valid
- geometry compatible
Full electromagnetic behavior supported.
C4 — Perfect Coherence (Ideal)#
- perfect divergence/curl stability
- perfect propagation stability
- perfect geometric compatibility
C4 is theoretical; real systems approach C3.
3. Collapse Modes (EM1 → EM5)#
Collapse occurs when coherence fails structurally.
EM1 — Divergence Collapse#
∇·E or ∇·B invalid.
EM2 — Curl Collapse#
∇×E or ∇×B invalid.
EM3 — Propagation Collapse#
Wave evolution unstable.
EM4 — Source Collapse#
Invalid charge/current configuration.
EM5 — Geometry Collapse#
Field‑geometry mismatch.
Collapse is structural, not force‑based.
4. Regime Behavior (R1 → R3)#
Coherence behaves differently across RTT regimes:
R1 — Classical Field Stability#
- static + quasi‑static fields
- divergence/curl stable
- no geometric coupling
Coherence dominated by divergence/curl consistency.
R2 — Dynamic Field Propagation#
- full Maxwell dynamics
- wave propagation
- time‑varying fields
Coherence dominated by propagation stability.
R3 — Geometry‑Coupled, Multi‑Scale EM#
- field tensor Fᵤᵥ active
- geometric propagation
- QFT compatibility
Coherence dominated by geometric invariants.
5. Coherence Evaluation Procedure#
To evaluate coherence:
- Validate divergence structure
- Validate curl structure
- Validate propagation stability
- Validate source compatibility
- Validate geometric compatibility
- Validate regime alignment
If any step fails → classify collapse mode.
6. Summary#
Electromagnetic coherence is:
- structural
- operator‑driven
- multi‑scale
- geometry‑embedded
- regime‑aware
- zero drift
Electromagnetism = coherent field behavior.
Light = self‑consistent field propagation.
Physics = operator‑driven coherence systems.